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Energy Methods (energy + methods)

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Mathematics and Statistics	50%

Selected Abstracts

Comment on the connected-moments polynomial approach

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2008
M. G. Marmorino
Abstract Bartashevich has recently proposed two new methods for approximating eigenvalues of a Hamiltonian. The first method uses Hamiltonian moments generated from a trial function and his second method is a generalization of local energy methods. We show that the first method is equivalent to a variational one, a matrix eigenvalue problem using a Lanzcos subspace. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source]

Convergence rates toward the travelling waves for a model system of the radiating gas

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2007
Masataka Nishikawa
Abstract The present paper is concerned with an asymptotics of a solution to the model system of radiating gas. The previous researches have shown that the solution converges to a travelling wave with a rate (1 + t),1/4 as time t tends to infinity provided that an initial data is given by a small perturbation from the travelling wave in the suitable Sobolev space and the perturbation is integrable. In this paper, we make more elaborate analysis under suitable assumptions on initial data in order to obtain shaper convergence rates than previous researches. The first result is that if the initial data decays at the spatial asymptotic point with a certain algebraic rate, then this rate reflects the time asymptotic convergence rate. Precisely, this convergence rate is completely same as the spatial convergence rate of the initial perturbation. The second result is that if the initial data is given by the Riemann data, an admissible weak solution, which has a discontinuity, converges to the travelling wave exponentially fast. Both of two results are proved by obtaining decay estimates in time through energy methods with suitably chosen weight functions. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Compact difference schemes for heat equation with Neumann boundary conditions

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2009
Zhi-Zhong Sun
Abstract In this article, two recent proposed compact schemes for the heat conduction problem with Neumann boundary conditions are analyzed. The first difference scheme was proposed by Zhao, Dai, and Niu (Numer Methods Partial Differential Eq 23, (2007), 949,959). The unconditional stability and convergence are proved by the energy methods. The convergence order is O(,2 + h2.5) in a discrete maximum norm. Numerical examples demonstrate that the convergence order of the scheme can not exceeds O(,2 + h3). An improved compact scheme is presented, by which the approximate values at the boundary points can be obtained directly. The second scheme was given by Liao, Zhu, and Khaliq (Methods Partial Differential Eq 22, (2006), 600,616). The unconditional stability and convergence are also shown. By the way, it is reported how to avoid computing the values at the fictitious points. Some numerical examples are presented to show the theoretical results. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source]

An assessment of urologists' training and knowledge of energy-based surgical devices

BJU INTERNATIONAL, Issue 2 2008
Daniel S. Lehman
OBJECTIVE To assess surgeons' training and current understanding of existing energy-based surgical instrumentation (ESI), we disseminated an online questionnaire to urology residents, fellows and attending urologists. SUBJECTS AND METHODS A two part 24-question survey was disseminated to 1000 urology residents, fellows and attending physicians. The first part of the questionnaire assessed the respondents' demographics and education about ESI; the second part evaluated the respondent's knowledge of surgical energy methods and ESI, and was stratified into nine basic- and six advanced-knowledge questions. RESULTS In all, 136 people (13.6%) viewed the survey and it was completed by 63 (6.3%). Respondents comprised 27 (43%) attending physicians, 14 (22%) minimally-invasive urology fellows and 22 (35%) urology residents. Among participants, 41 (64%) had received no formal didactic training on ESI, and a further 14% of respondents' didactic experience was limited to one lecture. Of the respondents, 70% said that monopolar energy was the mode most often used in surgery. Overall, the participants correctly answered 41% of the questions. Of the nine questions classified as ,basic' knowledge, respondents correctly answered 49%. Of the six questions classified as ,advanced' knowledge, 29% were answered correctly. The highest percentage score was obtained by the attending urologists, with a mean (range) score of 41 (29,86)%, followed by the fellows, with a mean score of 39.5 (29,57)%, and then the residents, at 34 (14,64)%. CONCLUSION Despite widespread and growing use of ESI, there is currently minimal formal training on energy modes and current energy devices being provided to urological surgeons. Both practising and training urologists have a limited understanding of surgical energy modes and of existing ESI. [source]